Question: Reduce to lowest terms: $- \dfrac{7}{5} \div \dfrac{8}{9} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{8}{9}$ is $ \dfrac{9}{8}$ Therefore: $ - \dfrac{7}{5} \div \dfrac{8}{9} = - \dfrac{7}{5} \times \dfrac{9}{8} $ $ \phantom{- \dfrac{7}{5} \times \dfrac{9}{8}} = \dfrac{-7 \times 9}{5 \times 8} $ $ \phantom{- \dfrac{7}{5} \times \dfrac{9}{8}} = \dfrac{-63}{40} $